Less than a month before its opening date, huge swathes of the Tate Modern at Bankside were still more a site than a building and contingents of gallery assistants and service workers trooped through the corridors en route to training sessions. Eighty-four or so individual galleries means 84 gallery assistants on duty all the time.

Still, it looks as if it will all be alright on the night of May 11th, when several thousand guests, including not only business sponsors, politicians and art stars such as David Hockney, Rachel Whiteread and Damien Hirst, but also actors and musical celebrities including Madonna, Mick Jagger, Johnny Depp, Elton John, David Bowie and Bjork, turn up for the inaugural bash that has somehow become the hottest ticket in the year 2000.

It should be a moment to savour for Sir Nicholas Serota, Tate director - but not, as it happens, director of Tate Modern - and the person who, more than any other, can claim to be personally responsible for the £134 million Bankside project.

For him, the official opening will be the culmination of a process that began as far back as the late 1980s, when it became clear that the Tate needed a great deal more space to do justice to its superlative collection of modern art.

The first thing that strikes you about Bankside is its sheer scale. It looms threateningly over you as you approach it. Like a piece of totalitarian architecture, it is a huge dark slab of a building, its brown brick stained nearly black by London's polluted air, its incredibly long facade interrupted only by a dizzily high chimney. During its years of dereliction, it was judged sufficiently forbidding to serve as a backdrop for the films Judge Dredd and Richard III.

Its designer, Sir Giles Gilbert Scott, was also responsible for creating a British icon, in the form of the red telephone box. The building was converted by Swiss architects Herzog & de Meuron and one joke has it that their best known building prior to the Tate, the signal box at Basel's main railway station, wasn't much bigger than a telephone box.

Bankside was built in 1953 and ceased to function in 1981, when the oil needed to drive its turbine generators became prohibitively expensive. One part of the complex, however, the Switch House, is still owned by London Electricity and still functions as a transformer - this accounts for the hum that is audible throughout the building, and becomes a loud roar once you are outside at the back.

In adapting the space, Herzog and de Meuron have preserved a sense of its industrial past and its scale by their choice of materials and finishes (concrete, steel and untreated wood), and by leaving the vast turbine hall, which is about a third of the overall building and runs for its full, 500 foot length, empty, save for a bridge that cuts across it at ground level. The turbine hall will also contain one work of art - albeit a suitably monumental one.

In the weeks before the opening the huge hall resounded deafeningly to the hammer blows of metal workers assembling this work, the first in a series of specially commissioned, "wowish" sculptures: a trio of observation towers and a giant spider, designed by Louise Bourgeois, an artist whose career spans the 20th century. The whole enormous chamber, overlooked by the various adjoining floors, is a soaring, cathedral-like space.

Which brings us to the second thing you cannot help but notice about the Tate Modern: its strategic location opposite Christopher Wren's St Paul's Cathedral on the north bank of the river. While the church nestles comfortably in London's commercial heart, the gallery lies in the altogether less salubrious borough of Southwark, but soon the two will be symbolically and physically linked by the first new bridge over the Thames to be built in central London since 1894. Well under way, it will be an elegant structure for pedestrian traffic, designed jointly by architect Norman Foster, engineers Ove Arup and sculptor Anthony Caro. Commentators have been quick to interpret this whole set-up as reflecting a shift in the balance of moral authority, as art becomes a repository of spiritual value in a secular age.

In fact, as the structure and organisation of the Tate demonstrates, things are not quite so clear-cut. It is truer to say that, strategically poised at the start of a new millennium, in the western world both enterprises are riddled with doubt. Both are vigorously contested spaces.

This became clear when the Bankside team started thinking about how they should exhibit the work in their permanent collections (Bankside's temporary exhibitions programme doesn't kick off until the year 2001). While it is generally acknowledged that the Tate has one of the world's leading collections of 20th century art at its disposal, the question facing chief curator Francis Morris was how they should go about displaying it in the aftermath of Modernism.

After prolonged debate on a number of potential strategies, the solution eventually arrived at draws on current curatorial thinking in its avoidance of predictable canons and simple chronology.

Instead, work from right through the 20th century will be displayed thematically in terms of the four genres established by the French Academy in the 17th century, not so much to underline the perseverance of those categories as to demonstrate how they have been reinterpreted, transformed and transcended throughout the last 100 and more years. They are Landscape, Still Life, The Nude and History Painting, and a suite of galleries is devoted to each.

All this had been decided, and all decisions about the layout of the galleries had been taken, when a director of the Tate Modern was appointed in 1998. He is, perhaps surprisingly, not English but a Swede, Lars Nittve, and his appointment prompted Private Eye to point out that it was "the first time a root vegetable has been given a major role in the arts in Britain," identifying the Tate as a "Museum of Modern Garbage . . . in the heart of London's no-man's-land".

Nittve had come from one of the best modern art museums in the world, Denmark's Louisiana outside Copenhagen, and he had remarked that the Tate was just about the only job that would have drawn him away from it. He likes the fact that it is an industrial building and hence free of the baggage that comes with the great European culture palaces.

For many, the surprising thing about his appointment was not his nationality but the fact that the job was going to anybody other than Tate Millbank's director, Serota.

He remains, as one observer puts it, overlord of the Tate empire, and whether or not he would have liked the job of director of the Tate Modern, he very gracefully aligned himself with the move to appoint a younger person.

The Tate Modern may be the job of Nittve's dreams but it is likely to test his reserves. He can be grateful, however, for one thing: the building that Serota, Herzog and de Meuron have provided for him. Regardless of details of design and workmanship (there have been criticisms of both), the significance of their achievement is that they have managed to make a place that people will want to go and see for itself, because, like Everest, it is there. It is a compelling architectural object without being an outsider, an exotic showpiece like the Bilbao Guggenheim. And it provides a new slant on London.

Herzog and de Meuron's main addition to the building, apart of course from the provision of a vast network of flexible internal spaces, was the creation of what they call "the light beam": a new, full-length, two-storey glass structure on the roof. This brings light onto the top level galleries but also, from the restaurant on the top floor, provides stunning views north across and along the river. People will certainly visit just to eat and look out at the view. This is no minor point because, with free entry to the galleries, in the pragmatic, mixed-economy world of cultural funding, the mighty Tate Modern will depend to a significant extent on the revenue generated by its restaurants.

The Tate Modern at Bankside is open from May 12th.